In this paper, several identities concerning expectation, variance, covariance, cumulative distribution functions, the coefficient of variation, and the Lorenz curve are obtained and they are used in establishing theoretical results. Furthermore, a graphical representation of the variance is...

Building on the widely-used double-lognormal approach by Bahra (1997), this paper presents a multi-lognormal approach with restrictions to extract risk-neutral probability density functions (RNPs) for various asset classes. The contributions are twofold: first, on the technical side, the paper...

This paper develops a simple procedure for incorporating market-based information into the construction of fan charts. Using the International Monetary Fund (IMF)'s global growth forecast as a working example, the paper goes through the theoretical and practical considerations of this new...

In most macroeconomic models, the substitutability between domestic and foreign goods is calibrated using aggregated data. This imposes homogeneous elasticities across goods, and the calibration is only valid under this assumption. If elasticities are heterogeneous, the aggregate...

I introduce a new approach to modeling aggregate bidding functions (demand functions) submitted by participants of share auctions, the one based on (scaled) normal cumulative distribution functions. I provide a simple model illustrating how normal cdf-shaped demand might arise. Then, using new...